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Scientific Bulletin of Namangan State University

Abstract

In this paper conditions of asymptotic normality of the recursive estimate based on a random number of observations for derivative of multivariate probability density function are proved and these results are used for nonparametric confidence estimation by fixed-width confidence intervals for a derivative оf multivariate probability density function.

First Page

46

Last Page

52

References

1. Yamato H. Sequential estimation of a continuous probability density function and mode. Bull. Math. Statist. 14, 1-12 (1971). 2. Davies H. I. Strong consistency of a sequential estimation of a probability density function. Bull. Math. Statist. 15, 49-54 (1973). 3. Samanta M., Mugisha R. X. On a class of estimates of the probability density function and mode based on a random number of observations. Calcutta statistical association bulletin 30, N 117-118, 23-40 (1981). 4. Gixman I.I., Skoroxod A.V. “Vvedenie v teoriyu sluchaynix protsessov”, Moskva, Nauka, 1977. 5. Silvestrov D. S., Mirzaxmedov M. A., Tursunov G. T., “O primeneniyax predelnix teorem dlya slojnix sluchaynix funksiy k nekotorim zadacham statistiki”, Teoriya veroyatnostey i matematicheskaya statistika, 1976, 14, 124-137. 6. Silvestrov D. S., “Limit Theorems for Randomly Stopped Stochastic Processes”, Springer-Verlag, London, 2004.

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